The important applications of PET imaging in medical research, such as Parkinson disease, Schizophrenia, and drug addiction studies, have made the accurate quantitation of PET images essential, which is strongly impacted by the scattering events. While most current scattering correction techniques in PET are only adequate for some particular studies the goal of this investigation is to find a more universal scattering correction technique for a variety of activity distributions. It includes (1) developing two new scattering correction techniques in PET: position-dependent 2-dimensional scattering "deconvolution" (2-D SD) method and energy spectrum window (ESW) method, and (2) comparing them to the current scattering correction methods. The position-dependent 2-D SD method is based on the fact that the scattering occurs in both transaxial and axial directions and it can be modeled by a 2-D spatially-variant "deconvolution" in the method can be achieved by an iterative method. In the investigation, this technique will be compared to the 1-D deconvolution method and the current background fitting scattering technique which has been used in PENN-PET scanners in terms of accuracy of the correction, computation time of algorithm, practicality and the noise propagation. This kind of comparison is important since the 2-D SD method accounts best for local variations in the distribution while the background subtraction technique accounts best for out-of-field-of-view (FOV) scattering. Both the 2-D SD and background fitting techniques account well for cross-plane scattering, which is important since the volumetric imaging systems, such as PENN-PET scanners, have no septa in the FOV, while 1-D deconvolution is only adequate for a source which has a uniform distribution along the axial direction. A unique property of the PENN-PET scanner is that its detectors are made of NaI(TI) which provides a good photopeak energy resolution of less than 10% FWHM. Hence, the ESW method of SPECT can be adapted into the PET system. The basis for the technique is that information from other windows can be used to estimate the position-dependent scatter fraction under the photopeak window. The major difference from SPECT is that in PET a 2-dimensional coincidence spectrum defined by the energies of the detector pair will be used. By using this technique, both the cross- plane and out-of-FOV scattering can be compensated for as well as local variations in the activity distribution. This technique has not been applied to any PET system yet. The goal of this part of the project is (1) full evaluation of the ESW technique in PET and 92) implementation for the PENN-PET scanners. In addition, the effect of the random counts by using ESW technique and the signal-to-noise ratio before and after corrections will be studied. For both proposed scattering correction techniques, a Monte Carlo simulation, which is under development in another project, will be used to further compare techniques and provide evaluation which cannot be done with real data.